%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD024-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:11:30 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 27 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_4,VAR_5,VAR_2)
| ~ sum(VAR_3,VAR_5,VAR_1)
| ~ sum(VAR_0,VAR_3,VAR_4)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_1) ).
cnf(c_1,plain,
( ~ sum(E,F,C)
| ~ sum(D,F,B)
| ~ sum(A,D,E)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_1]) ).
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ sum(VAR_1,VAR_0,VAR_2)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_14,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(sum_3,axiom,
sum(b,additive_inverse(a),additive_identity),
file('theBenchmark.p',sum_3) ).
cnf(c_29,plain,
sum(b,additive_inverse(a),additive_identity),
inference(clausify,[status(thm)],[sum_3]) ).
fof(not_sum_4,axiom,
~ sum(additive_identity,a,b),
file('theBenchmark.p',not_sum_4) ).
cnf(c_30,plain,
~ sum(additive_identity,a,b),
inference(clausify,[status(thm)],[not_sum_4]) ).
cnf(c_59,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_115,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_116,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_154,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_375,plain,
( ~ sum(B,C,b)
| ~ sum(A,C,a)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_1,c_30]) ).
cnf(c_376,plain,
( ~ sum(additive_identity,A,b)
| ~ sum(additive_identity,A,a) ),
inference(resolve,[status(thm)],[c_375,c_59]) ).
cnf(c_343,plain,
~ sum(additive_identity,b,a),
inference(resolve,[status(thm)],[c_376,c_154]) ).
cnf(c_365,plain,
~ sum(b,additive_identity,a),
inference(resolve,[status(thm)],[c_5,c_343]) ).
cnf(c_377,plain,
( ~ sum(B,C,a)
| ~ sum(A,C,additive_identity)
| ~ sum(b,A,B) ),
inference(resolve,[status(thm)],[c_1,c_365]) ).
cnf(c_378,plain,
( ~ sum(additive_identity,A,a)
| ~ sum(additive_inverse(a),A,additive_identity) ),
inference(resolve,[status(thm)],[c_377,c_29]) ).
cnf(c_379,plain,
~ sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_378,c_116]) ).
cnf(c_374,plain,
$false,
inference(resolve,[status(thm)],[c_115,c_379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD024-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n013.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 02:23:21 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 4009114 was started by sandbox2 on n013,
% 0.15/0.42 % Sun Sep 27 02:23:21 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.48
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48
% 0.15/0.48 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.48 % Length of proof is 16.
% 0.15/0.48 % Level of proof is 4.
% 0.15/0.48 % Maximum clause weight is 21.000.
% 0.15/0.48 % Given clauses 73.
% 0.15/0.48
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------